In Exercises 5–7, convert each angle in radians to degrees.7𝜋5

Verified step by step guidance

1. Understand the relationship between radians and degrees: 180 degrees is equivalent to \( \pi \) radians.
2. To convert radians to degrees, use the formula: \( \text{degrees} = \text{radians} \times \frac{180}{\pi} \).
3. Substitute the given radian value into the formula: \( 7\pi/5 \times \frac{180}{\pi} \).
4. Simplify the expression by canceling out \( \pi \) from the numerator and the denominator.
5. Multiply the remaining numbers to find the angle in degrees.

Key Concepts

Radians and Degrees

Radians and degrees are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. To convert between these units, one can use the relationship that 180 degrees equals π radians.

Conversion Formula

The conversion from radians to degrees can be performed using the formula: degrees = radians × (180/π). This formula allows for the straightforward transformation of an angle measured in radians into its equivalent in degrees.

Simplifying Fractions

When converting angles, it is often necessary to simplify fractions. For example, when converting 7π/5 radians to degrees, one should first multiply by the conversion factor and then simplify the resulting fraction to express the angle in a more standard form.